Word Problem with Equal Lengths

Question

Paul has three pieces of rope with lengths of 140cm, 168cm and 210cm.  He wishes to cut the three pieces of rope into smaller pieces of equal length with no remainders.  (a) What is the greatest possible length of each of the smaller pieces of rope?   (b) How many of the smaller pieces of rope of equal length can he get altogether? 

Answer 1

What is the greatest common factor (GCF) of the three numbers?

Answer 2

140 = 2(70) = 2(2)(35) =  2(2)(5)(7)= 14(10)

 

168 = 2(84) = 2(2)(42) = 2(2)(2)(21) = 2(2)(2)(3)(7) = 14(12)

 

210 = 3(70) = 3(7)(10) = 3(7)(2)(5) = 2(3)(5)(7) = 14(15)

 

then, gcf(140,168,210) = 14 = greatest possible length of each of the smaller pieces of rope

 

also, there would then be how many such lengths of 14 altogether?

 

answer:  10 + 12 + 15 = 37